1. Field of the Invention
The present invention relates to a programmable gain Metal-Oxide-Semiconductor (MOS) amplifier, and more particularly, to a linear-to-dB programmable gain MOS amplifier.
2. Description of the Prior Art
Please refer to FIG. 1. FIG. 1 is a diagram illustrating a conventional linear-to-dB Bipolar-Junction-Transistor (BJT) amplifier 100. As shown in FIG. 1, the linear-to-dB BJT amplifier 100 comprises BJTs B1, B2, B3, and B4, and a resistor RB. The collector of the BJT B1 receives an input current signal IIN, the base of the BJT B1 receives a control current signal ICON, and the emitter of the BJT B1 is coupled to a biasing source VSS (for example, ground). The collector of the BJT B2 is coupled to a biasing source VDD, the base of the BJT B2 receives the input current signal IIN, and the emitter of the BJT B2 receives the control current signal ICON. The collector of the BJT B3 is coupled to the biasing source VDD, the base of the BJT B3 receives the input current signal IIN, and the emitter of the BJT B3 receives the control current signal ICON through the resistor RB. The first end of the resistor RB is coupled to the emitter of the BJT B3, and the second end of the resistor RB is coupled to the base of the BJT B4. The base of the BJT B4 is coupled to the second end of the resistor RB and receives the control current signal ICON, the emitter of the BJT B4 is coupled to the biasing source VSS, and the collector of the BJT B4 outputs the output current signal IOUT.
All the BJTs in FIG. 1 are appropriately biased, and thus, the relation between base-emitter voltages VBEs of all the BJTs can be described as an equation as follows:VBE1+VBE2=VBE3+ICON×RB+VBE4  (1),where VBE1 represents the base-emitter voltage of the BJT1, VBE2 represents the base-emitter voltage of the BJT2, VBE3 represents the base-emitter voltage of the BJT3, and VBE4 represents the base-emitter voltage of the BJT4. Since the relation between the base-emitter voltage VBE of a BJT and the current flowing from the BJT can be described as an equation as follows:IE=ISeVBE/VT  (2),where e represents natural exponent, IE represents the current flowing from the emitter of the BJT, VBE represents the base-emitter voltage of the BJT, VT represents the threshold voltage of the BJT, and the IS represents the saturation current of the BJT, the further equations can be derived from the equations (1) and (2):VT ln(IIN/IS)+VT ln(ICON/IS)=VT ln(ICON/IS)+ICON×RB+VT ln(IOUT/IS)  (3)ln(IOUT/IIN)=(−ICON×RB)/VT  (4)IOUT=IIN×e(−ICON×RB)/VT  (5)G100=e(−ICON×RB)/VT  (6)G100=20×(1/ln 10)×[(−ICON×RB)/VT](dB)  (7)where G100 represent the gain of the BJT amplifier 100, and the difference between the equations (6) and (7) is that G100 in equation (7) is expressed in dB (decibel). Therefore, according to the equation (7), the gain G100 of the BJT amplifier 100 can be adjusted in dB units by linearly adjusting the control current signal ICON. More particularly, the gain G100 of the BJT amplifier 100 can be adjusted in dB linearly as the control current signal ICON is linearly adjusted, which provides great convenience.
However, since the exponential characteristic does not exist between the gate-source voltage (VGS) of a MOS and its corresponding output current ID, it is complicated to achieve adjusting the gain in dB linearly by linearly adjusting the magnitude of the controlling signal with a MOS amplifier.